Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

The co-evolution of culturally inherited altruistic helping and cultural transmission under random group formation.

Limited migration results in kin selective pressure on helping behaviors under a wide range of ecological, demographic and life-history situations. However, such genetically determined altruistic helping can evolve only when migration is not too strong and group size is not too large. Cultural inheritance of helping behaviors may allow altruistic helping to evolve in groups of larger size because cultural transmission has the potential to markedly decrease the variance within groups and augment the variance between groups. Here, we study the co-evolution of culturally inherited altruistic helping behaviors and two alternative cultural transmission rules for such behaviors. We find that conformist transmission, where individuals within groups tend to copy prevalent cultural variants (e.g., beliefs or values), has a strong adverse effect on the evolution of culturally inherited helping traits. This finding is at variance with the commonly held view that conformist transmission is a crucial factor favoring the evolution of altruistic helping in humans. By contrast, we find that under one-to-many transmission, where individuals within groups tend to copy a "leader" (or teacher), altruistic helping can evolve in groups of any size, although the cultural transmission rule itself hitchhikes rather weakly with a selected helping trait. Our results suggest that culturally determined helping behaviors are more likely to be driven by "leaders" than by popularity, but the emergence and stability of the cultural transmission rules themselves should be driven by some extrinsic factors.

Reconeixement de punts clau en imatges mitjançant l'algorisme Random Ferns

Treball final de carrera basat en el reconeixement de punts clau en imatges mitjançant l'algorisme Random Ferns.

Comparing Random-based and k-Anonymity-Based Algorithms for Graph Anonymization

Recently, several anonymization algorithms have appeared for privacy preservation on graphs. Some of them are based on random-ization techniques and on k-anonymity concepts. We can use both of them to obtain an anonymized graph with a given k-anonymity value. In this paper we compare algorithms based on both techniques in orderto obtain an anonymized graph with a desired k-anonymity value. We want to analyze the complexity of these methods to generate anonymized graphs and the quality of the resulting graphs.

Cross-frequency coupling in EEG revealed by adaptive oscillation tracking.

Introduction: Neuronal oscillations have been the focus of increasing interest in the neuroscientific community, in part because they have been considered as a possible integrating mechanism through which internal states can influence stimulus processing in a top-down way (Engel et al., 2001). Moreover, increasing evidence indicates that oscillations in different frequency bands interact with one other through coupling mechanisms (Jensen and Colgin, 2007). The existence and the importance of these cross-frequency couplings during various tasks have been verified by recent studies (Canolty et al., 2006; Lakatos et al., 2007). In this study, we measure the strength and directionality of two types of couplings - phase-amplitude couplings and phase-phase couplings - between various bands in EEG data recorded during an illusory contour experiment that were identified using a recently-proposed adaptive frequency tracking algorithm (Van Zaen et al., 2010). Methods: The data used in this study have been taken from a previously published study examining the spatiotemporal mechanisms of illusory contour processing (Murray et al., 2002). The EEG in the present study were from a subset of nine subjects. Each stimulus was composed of 'pac-man' inducers presented in two orientations: IC, when an illusory contour was present, and NC, when no contour could be detected. The signals recorded by the electrodes P2, P4, P6, PO4 and PO6 were averaged, and filtered into the following bands: 4-8Hz, 8-12Hz, 15-25Hz, 35-45Hz, 45-55Hz, 55-65Hz and 65-75Hz. An adaptive frequency tracking algorithm (Van Zaen et al., 2010) was then applied in each band in order to extract the main oscillation and estimate its frequency. This additional step ensures that clean phase information is obtained when taking the Hilbert transform. The frequency estimated by the tracker was averaged over sliding windows and then used to compare the two conditions. Two types of cross-frequency couplings were considered: phase-amplitude couplings and phase-phase couplings. Both types were measured with the phase locking value (PLV, Lachaux et al., 1999) over sliding windows. The phase-amplitude couplings were computed with the phase of the low frequency oscillation and the phase of the amplitude of the high frequency one. Different coupling coefficients were used when measuring phase-phase couplings in order to estimate different m:n synchronizations (4:3, 3:2, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1 and 9:1) and to take into account the frequency differences across bands. Moreover, the direction of coupling was estimated with a directionality index (Bahraminasab et al., 2008). Finally, the two conditions IC and NC were compared with ANOVAs with 'subject' as a random effect and 'condition' as a fixed effect. Before computing the statistical tests, the PLV values were transformed into approximately normal variables (Penny et al., 2008). Results: When comparing the mean estimated frequency across conditions, a significant difference was found only in the 4-8Hz band, such that the frequency within this band was significantly higher for IC than NC stimuli starting at ~250ms post-stimulus onset (Fig. 1; solid line shows IC and dashed line NC). Significant differences in phase-amplitude couplings were obtained only when the 4-8 Hz band was taken as the low frequency band. Moreover, in all significant situations, the coupling strength is higher for the NC than IC condition. An example of significant difference between conditions is shown in Fig. 2 for the phase-amplitude coupling between the 4-8Hz and 55-65Hz bands (p-value in top panel and mean PLV values in the bottom panel). A decrease in coupling strength was observed shortly after stimulus onset for both conditions and was greater for the condition IC. This phenomenon was observed with all other frequency bands. The results obtained for the phase-phase couplings were more complex. As for the phase-amplitude couplings, all significant differences were obtained when the 4-8Hz band was considered as the low frequency band. The stimulus condition exhibiting the higher coupling strength depended on the ratio of the coupling coefficients. When this ratio was small, the IC condition exhibited the higher phase-phase coupling strength. When this ratio was large, the NC condition exhibited the higher coupling strength. Fig. 3 shows the phase-phase couplings between the 4-8Hz and 35-45Hz bands for the coupling coefficient 6:1, and the coupling strength was significantly higher for the IC than NC condition. By contrast, for the coupling coefficient 9:1 the NC condition gave the higher coupling strength (Fig. 4). Control analyses verified that it is not a consequence of the frequency difference between the two conditions in the 4-8Hz band. The directionality measures indicated a transfer of information from the low frequency components towards the high frequency ones. Conclusions: Adaptive tracking is a feasible method for EEG analyses, revealing information both about stimulus-related differences and coupling patterns across frequencies. Theta oscillations play a central role in illusory shape processing and more generally in visual processing. The presence vs. absence of illusory shapes was paralleled by faster theta oscillations. Phase-amplitude couplings were decreased more for IC than NC and might be due to a resetting mechanism. The complex patterns in phase-phase coupling between theta and beta/gamma suggest that the contribution of these oscillations to visual binding and stimulus processing are not as straightforward as conventionally held. Causality analyses further suggest that theta oscillations drive beta/gamma oscillations (see also Schroeder and Lakatos, 2009). The present findings highlight the need for applying more sophisticated signal analyses in order to establish a fuller understanding of the functional role of neural oscillations.

Multidelayed random walks: Theory and application to the neolithic transition in Europe

We present a model in which particles (or individuals of a biological population) disperse with a rest time between consecutive motions (or migrations) which may take several possible values from a discrete set. Particles (or individuals) may also react (or reproduce). We derive a new equation for the effective rest time T˜ of the random walk. Application to the neolithic transition in Europe makes it possible to derive more realistic theoretical values for its wavefront speed than those following from the single-delayed framework presented previously [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)]. The new results are consistent with the archaeological observations of this important historical process

Time-delayed fronts from biased random walks

We generalize a previous model of time-delayed reaction–diffusion fronts (Fort and Méndez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc

On the convergence of EM-like algorithms for image segmentation using Markov random fields.

Inference of Markov random field images segmentation models is usually performed using iterative methods which adapt the well-known expectation-maximization (EM) algorithm for independent mixture models. However, some of these adaptations are ad hoc and may turn out numerically unstable. In this paper, we review three EM-like variants for Markov random field segmentation and compare their convergence properties both at the theoretical and practical levels. We specifically advocate a numerical scheme involving asynchronous voxel updating, for which general convergence results can be established. Our experiments on brain tissue classification in magnetic resonance images provide evidence that this algorithm may achieve significantly faster convergence than its competitors while yielding at least as good segmentation results.

Monte Carlo study of a kinetic lattice model with random diffusion of disorder

We report Monte Carlo results for a nonequilibrium Ising-like model in two and three dimensions. Nearest-neighbor interactions J change sign randomly with time due to competing kinetics. There follows a fast and random, i.e., spin-configuration-independent diffusion of Js, of the kind that takes place in dilute metallic alloys when magnetic ions diffuse. The system exhibits steady states of the ferromagnetic (antiferromagnetic) type when the probability p that J>0 is large (small) enough. No counterpart to the freezing phenomena found in quenched spin glasses occurs. We compare our results with existing mean-field and exact ones, and obtain information about critical behavior.

A random linear functional approach to efficiency bounds

This paper suggests a method for obtaining efficiency bounds in models containing either only infinite-dimensional parameters or both finite- and infinite-dimensional parameters (semiparametric models). The method is based on a theory of random linear functionals applied to the gradient of the log-likelihood functional and is illustrated by computing the lower bound for Cox's regression model